Nontrivial solutions for higher order multi-point boundary value problems - Zhang, Xinguang; Liu, L. (Elsevier, 2008)
In the case where a nonlinearity may change sign and contains higher derivatives, we consider the existence of nontrivial solutions for a class of higher order multi-point boundary value problems. Some sufficient conditions for the existence of nontrivial solutions are established under certain suitable growth conditions, our proof is based on Leray–Schauder nonlinear alternative.